On the behavior of the algebraic transfer期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the behavior of the algebraic transfer

Authors:	Robert R Bruner Lê M Hà Nguyê n H V Hung

Institution:	Department of Mathematics, Wayne State University, 656 W. Kirby Street, Detroit, Michigan 48202 ; Université de Lille I, UFR de Mathématiques, UMR 8524, 59655 Villeneuve d'Ascq Cédex, France ; Department of Mathematics, Vietnam National University, 334 Nguyên Trãi Street, Hanoi, Vietnam

Abstract:	Let $Tr_k:\mathbb{F}_2\underset{GL_k}{\otimes} PH_i(B\mathbb{V}_k)\to Ext_{\mathcal{A}}^{k,k+i}(\mathbb{F}_2, \mathbb{F}_2)$ be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer $tr_k: \pi_^S((B\mathbb{V} _k)_+) \to \pi_^S(S^0)$ . It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that is an isomorphism for . However, Singer showed that is not an epimorphism. In this paper, we prove that does not detect the nonzero element $g_s\in Ext_{\mathcal{A}}^{4,12\cdot 2^s}(\mathbb{F}_2, \mathbb{F}_2)$ for every $s\geq 1$ . As a consequence, the localized $(Sq^0)^{-1}Tr_4$ given by inverting the squaring operation is not an epimorphism. This gives a negative answer to a prediction by Minami.

Keywords:	Adams spectral sequences Steenrod algebra invariant theory algebraic transfer

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文